This is the title of a recently published monograph by Dr Max Stephens of the Melbourne Graduate School of Education at the University of Melbourne.

Some quotes:

In those classrooms where the focus is perceived to be on rewarding those who are successful at mathematics, it is easy for those who see themselves as unsuccessful to opt out. Likewise, those who see mathematics as difficult or confusing, or as a source of failure and criticism, are likely to lose interest.

Because of their experiences many of these students have built up negative behaviours and negative thoughts toward the learning of mathematics that are difficult to dislodge. Unless teachers work together and create a school and classroom culture that respects diversity, encourages effort and rewards improvement these students will slip further behind.

Stephens defines ‘engagement’ as “how mathematical ideas are explored, explained and elaborated—especially in a strong collective sense”. He goes on to assert:

Terms like ‘engaged’ and ‘engagement’ can be used rather loosely. Claims that students are—or appear to be—engaged need to be unpacked by asking: ‘What do you mean? Are students simply paying attention? Do they look busy? Are they merely doing what the teacher asks? Do they appear to understand what they are doing? Do they give evidence of liking or enjoying what they are doing?’ Some mathematics classes achieve an apparent engagement by having all students occupied in ‘busy work’. This can be done by
having students ‘engaged’ for large amounts of time completing worksheets or working through a textbook. Worksheets and textbooks have a place, but when they become tools for engagement—where students are expected to work quietly on their own, where the teacher’s role largely becomes one of providing individual assistance—these forms of engagement come at a cost.

Many classes can create a veneer of engagement in the same ways that the way we assess can create a “veneer of accomplishment’ (Lorna Earl). Our curriculum and our methodology need to be documented in such a way that good practice is embedded. This is too important to leave to chance and the variability of individual teachers. I believe that a certain methodology should be mandated. Every teacher needs to have, for example, a plan of how they will determine and activate prior knowledge, how they will ‘hook’ students into the mathematics to be explored(not merely an ‘engaging’ task – in terms of ‘fun’ or accessibility or busy work – but one that also sets the framework for the underlying mathematical concepts and/or skills), how they will explicitly teach the new material and how they will check for understanding along the way.

Another article that may be of interest, and along a related theme, is the CSE Occasional Paper No 121 (July 2011) by Vic Zbar titled Ensuring a More Personalised Approach: A strategy for differentiated teaching in schools. In this article, Table 1 shows a model of explicit instruction developed by Hume Secondary College (with John Hattie, I believe) which has become my new favourite thing. Differentiated teaching doesn’t mean having 25 different plans, it means having one good inclusive plan. I was so impressed with this table that I had it typed up separately to show to teachers (attached Explicit Instruction model).

More from Stephens:

…a little direct teaching is followed by setting tasks from worksheets or a textbook for all students. Students can appear to be engaged in such work. They know that they will rarely be asked to explain their thinking to the whole class, because the focus is on individual work. Students can sit next to friends and mix some quiet social conversation with the work in hand. If students are using a textbook, they can check if their answers are correct by checking at the back of the book. Occasionally they can ask the teacher a question, but usually the teacher is busy dealing with needier students or with those who are disruptive or off-task. By an unstated agreement the focus has come to be one of getting work done in an apparently quiet and well-managed class. We are not talking here about individual lessons, but about patterns of instruction that repeat themselves daily

How often do our students have to explain or make their thinking visible in our classrooms? What do we really value in our discipline? To support students becoming more creative, less dependent, greater risk-takers and more ‘engaged’, what do we actually do in our classrooms? What should they look like to better encourage the latter learning behaviours?

In the second half of the monograph, Stephens refers to three forms of scaffolding that teachers should be aware of in designing their lessons and better supporting student learning (my emphasis via bold type):

Three different kinds of scaffolding: Baxter and Williams (2010) refer to the first as analytic scaffolding. This is intended to help students understand mathematical ideas, with their related skills and procedures, so that mathematics makes sense to them—a proposition that is also supported by Meyer and Turner (2002).The second form of scaffolding is intended to create classroom communities where students can work together and to think more broadly and deeply than if everyone was left working on their own. Baxter and Williams refer to this as social scaffolding. The third kind of scaffolding focuses on helping each student to develop a sense of ownership of what they are learning. In particular, teachers need to encourage students to take charge of their learning and to be engaged because they want to learn mathematics. Scaffolding in this third sense implies giving enough support to enable students to grow in self-confidence but not too much as to inhibit risk taking and independence.

How well are we providing these three types of scaffolding in our classes? How does our assessment (formative and summative) contribute to these?

Lots of interesting thinking here. And timely. What can be put in place for 2012 in your classes? Your school?

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About Linda

I have been involved in secondary mathematics education in Victoria, Australia for over 25 years.